asianbystt

Price Asian options using standard trinomial tree

Syntax

Price = asianbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates)

Price = asianbystt(___,AmericanOpt,AvgType,AvgPrice,AvgDate)

Description

Price = asianbystt(STTTree,OptSpec,Strike,Settle,ExerciseDates) prices Asian options using a standard trinomial (STT) tree.

Price = asianbystt(___,AmericanOpt,AvgType,AvgPrice,AvgDate) prices Asian options using a standard trinomial (STT) tree with optional arguments for AmericanOpt, AvgType, AvgPrice, and AvgDate.

Examples

Price an Asian Option Using the Standard Trinomial Tree Model

Create a RateSpec.

StartDates = 'Jan-1-2009'; 
EndDates = 'Jan-1-2013'; 
Rates = 0.035; 
Basis = 1; 
Compounding = -1;
RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,...
'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.8694
            Rates: 0.0350
         EndTimes: 4
       StartTimes: 0
         EndDates: 735235
       StartDates: 733774
    ValuationDate: 733774
            Basis: 1
     EndMonthRule: 1

Create a StockSpec.

AssetPrice = 85; 
Sigma = 0.15; 
StockSpec = stockspec(Sigma, AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1500
         AssetPrice: 85
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Create an STTTree.

NumPeriods = 4;
TimeSpec = stttimespec(StartDates, EndDates, 4);
STTTree = stttree(StockSpec, RateSpec, TimeSpec)

STTTree = struct with fields:
       FinObj: 'STStockTree'
    StockSpec: [1x1 struct]
     TimeSpec: [1x1 struct]
     RateSpec: [1x1 struct]
         tObs: [0 1 2 3 4]
         dObs: [733774 734139 734504 734869 735235]
        STree: {1x5 cell}
        Probs: {[3x1 double]  [3x3 double]  [3x5 double]  [3x7 double]}

Define the Asian option and compute the price.

Settle = '01-Jan-2009';
ExerciseDates = [datenum('1/1/12');datenum('1/1/13')];
OptSpec = 'call';
Strike = 100;

Price = asianbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)

Price = 2×1

    1.6905
    2.6203

Input Arguments

STTTree — Stock tree structure for standard trinomial tree

structure

Stock tree structure for a standard trinomial tree, specified by using stttree.

Data Types: struct

OptSpec — Definition of option

character vector with value 'call' or 'put'

Definition of option, specified as 'call' or 'put' using a character vector.

Data Types: char

Strike — Option strike price value

matrix of nonnegative integers

Option strike price value, specified with a nonnegative integer using a NINST-by-1 matrix of strike price values. To compute the value of a floating-strike Asian option, Strike should be specified as NaN. Floating-strike Asian options are also known as average strike options.

Data Types: double

Settle — Settlement date or trade date

serial date number | date character vector

Settlement date or trade date for the Asian option, specified as a NINST-by-1 matrix of settlement or trade dates using serial date numbers or date character vectors.

Note

The Settle date for every Asian option is set to the ValuationDate of the stock tree. The Asian argument, Settle, is ignored.

Data Types: double | char

ExerciseDates — Option exercise dates

serial date number | date character vector

Option exercise dates, specified as a serial date number or date character vector:

• For a European option, use aNINST-by-1 matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only one ExerciseDates on the option expiry date.

• For an American option, use a NINST-by-2 vector of exercise date boundaries. The option can be exercised on any tree date between or including the pair of dates on that row. If only one non-NaN date is listed, or if ExerciseDates is a NINST-by-1 vector of serial date numbers or cell array of character vectors, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

Data Types: double | char

AmericanOpt — Option type

0 European (default) | scalar with values [0,1]

Option type, specified as NINST-by-1 positive integer scalar flags with values:

• 0 — European

• 1 — American

Data Types: single | double

AvgType — Average types

arithmetic (default) | character vector with values of arithmetic or geometric

Average types, specified as arithmetic for arithmetic average, or geometric for geometric average.

Data Types: char

AvgPrice — Average price of underlying asset at Settle

scalar

Average price of underlying asset at Settle, specified as a scalar.

Note

Use this argument when AvgDate < Settle.

Data Types: double

AvgDate — Date averaging period begins

scalar

Date averaging period begins, specified as a scalar.

Data Types: double

Output Arguments

Price — Expected prices for Asian options at time 0

matrix

Expected prices for Asian options at time 0, returned as a NINST-by-1 matrix. Pricing of Asian options is done using Hull-White (1993). Consequently, for these options there are no unique prices on the tree nodes with the exception of the root node.

More About

Asian Option

An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option.

Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.

References

[1] Hull, J., and A. White. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives. Vol. 1, pp. 21–31.